An Explicit Representation of the Dominant Eigenstructure for Positive Operators on Banach Lattices
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911715028893696 |
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| author | Chino, Yuki Kinjo, Kensaku Oizumi, Ryo |
| author_facet | Chino, Yuki Kinjo, Kensaku Oizumi, Ryo |
| contents | The Riesz projection and the corresponding eigenfunction of a positive operator satisfying the Doeblin condition are explicitly constructed using the partial Bell polynomials. While classical Fredholm theory requires stringent summability conditions, such as the operator being in a Schatten class to ensure the convergence of Fredholm minors, our approach utilizes the local algebraic structure induced by the Doeblin condition. We define a scalar function $D(λ)$ whose derivative $D'(λ_0)$ at the dominant eigenvalue $λ_0$ naturally provides the normalization constant for the projection. Consequently, an explicit functional representation of the eigenfunction is obtained as a limit of a weighted ratio of the operator's kernel, bypassing the need to solve transcendental characteristic equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_11723 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Explicit Representation of the Dominant Eigenstructure for Positive Operators on Banach Lattices Chino, Yuki Kinjo, Kensaku Oizumi, Ryo Functional Analysis The Riesz projection and the corresponding eigenfunction of a positive operator satisfying the Doeblin condition are explicitly constructed using the partial Bell polynomials. While classical Fredholm theory requires stringent summability conditions, such as the operator being in a Schatten class to ensure the convergence of Fredholm minors, our approach utilizes the local algebraic structure induced by the Doeblin condition. We define a scalar function $D(λ)$ whose derivative $D'(λ_0)$ at the dominant eigenvalue $λ_0$ naturally provides the normalization constant for the projection. Consequently, an explicit functional representation of the eigenfunction is obtained as a limit of a weighted ratio of the operator's kernel, bypassing the need to solve transcendental characteristic equations. |
| title | An Explicit Representation of the Dominant Eigenstructure for Positive Operators on Banach Lattices |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2602.11723 |